A firm expects to pay dividends at the end of each of the next four years of $2.00,$1.50,$2.50,and $3.50.If growth is then expected to level off at 8 percent,and if you require a 14 percent rate of return,how much should you be willing to pay for this stock?
A) $67.81
B) $22.49
C) $58.15
D) $31.00
E) $43.97

Question

Quizplus · Accepted Answer

To determine the value of the stock, we use the dividend discount model for a stock with non-constant growth initially, followed by constant growth. First, we find the present value of the dividends during the non-constant growth period:- Year 1 Dividend: $2.00 / (1 + 0.14)^1 = $1.75- Year 2 Dividend: $1.50 / (1 + 0.14)^2 = $1.15- Year 3 Dividend: $2.50 / (1 + 0.14)^3 = $1.73- Year 4 Dividend: $3.50 / (1 + 0.14)^4 = $2.15Next, we calculate the present value of the stock at the end of Year 4, just before it begins to grow at a constant rate. This is done using the Gordon Growth Model (also known as the Dividend Growth Model for a perpetuity with growth):$$ P_4 = \frac{D_5}{r - g} = \frac{3.50 \times (1 + 0.08)}{0.14 - 0.08} = \frac{3.78}{0.06} = \$63.00 $$Then, we discount this value back to the present:$$ PV = \frac{\$63.00}{(1 + 0.14)^4} = \$36.12 $$Finally, we sum up the present values of the dividends and the discounted value of the stock:$$ Total Value = \$1.75 + \$1.15 + \$1.73 + \$2.15 + \$36.12 = \$43.90 $$The calculation closely matches option E) $43.97, considering slight differences could be due to rounding at different steps.

A Firm Expects to Pay Dividends at the End of Each